YES(?,O(n^2))

Problem:
 +(x,+(y,z)) -> +(+(x,y),z)
 +(*(x,y),+(x,z)) -> *(x,+(y,z))
 +(*(x,y),+(*(x,z),u)) -> +(*(x,+(y,z)),u)

Proof:
 Matrix Interpretation Processor:
  dimension: 2
  interpretation:
                 [1 9]          [0]
   [*](x0, x1) = [0 1]x0 + x1 + [5],
   
                      [1 1]     [0]
   [+](x0, x1) = x0 + [0 1]x1 + [2]
  orientation:
                     [1 1]    [1 2]    [2]        [1 1]    [1 1]    [0]              
   +(x,+(y,z)) = x + [0 1]y + [0 1]z + [4] >= x + [0 1]y + [0 1]z + [4] = +(+(x,y),z)
   
                      [2  10]        [1 2]    [2]    [1 9]        [1 1]    [0]              
   +(*(x,y),+(x,z)) = [0  2 ]x + y + [0 1]z + [9] >= [0 1]x + y + [0 1]z + [7] = *(x,+(y,z))
   
                           [1 2]    [2  19]        [1 1]    [7 ]    [1 1]    [1 9]        [1 1]    [0]                   
   +(*(x,y),+(*(x,z),u)) = [0 1]u + [0  2 ]x + y + [0 1]z + [14] >= [0 1]u + [0 1]x + y + [0 1]z + [9] = +(*(x,+(y,z)),u)
  problem:
   
  Qed